Spatial accuracy correction method and apparatus

ABSTRACT

A spatial accuracy correction apparatus performs a spatial accuracy correction of a positioner displacing a displacer to a predetermined set of spatial coordinates using a measurable length value measured by an interferometer and a measurable value of the set of spatial coordinates of the displacement body that is measured by the positioner. The measured length value and the measured value for each measurement point are acquired by displacing the displacement body to a plurality of measurement points in order, one or more repeated measurements are conducted for at least one of the plurality of measurement points being measured after conducting measurement of the measured length value and the measured value for each of the plurality of measurement points, and the plurality of points are measured again when a repeat error of the measured length value is equal to or greater than a threshold value.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. § 119 ofJapanese Application No. 2017-240065, filed on Dec. 14, 2017, thedisclosure of which is expressly incorporated by reference herein in itsentirety.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a spatial accuracy correction methodand apparatus that correct an error in positioning in a positioningmechanism that positions a displacement body at a predetermined set ofspatial coordinates.

2. Description of Related Art

Conventionally, a positioning mechanism is known that positions(displaces) a displacement body at a predetermined coordinate positionin space (spatial coordinates). Examples of such positioning mechanismsmay include a coordinate measuring machine (CMM) that displaces ameasurement probe to measure a shape of an object, a machine tool thatdisplaces a processing tool to process an object, a robot that displacesan arm to a predetermined position, and the like.

In a positioning mechanism of this kind, a displacement body must bepositioned accurately at a predetermined set of spatial coordinates, andin order to achieve this, spatial accuracy correction methods have beenproposed in which, for each axis in a positioning mechanism,translational error, rotational error, and squareness error between axesis corrected appropriately, and errors in positioning are reduced (see,for example, Umetsu et al. (2005) and the specification of German PatentNo. 102007004934). The method described in Umetsu et al. performsspatial accuracy correction with a multilateration method, using atracking-type laser interferometer. In addition, the method described inGerman Patent No. 102007004934 changes a position of a retroreflectorattached to a tip of a Z spindle of a CMM to four or more locations, andmeasures the positions of the retroreflector in each location using theCMM. Also, simultaneously with this, a change in a distance to theretroreflector is measured by a tracking-type laser interferometer thatis within a measurement range of the CMM or positioned in the vicinitythereof. Then, based on these measured values, a position of a rotationcenter of the tracking-type laser interferometer and an absolutedistance from the rotation center of the tracking-type laserinterferometer to the retroreflector are calculated with themultilateration method.

Here, a spatial accuracy correction method of a conventional positioningmechanism is described concretely. FIG. 4 illustrates a spatial accuracycorrection apparatus that carries out the spatial accuracy correctionmethod of the positioning mechanism (in this example, a CMM 10 isdescribed). In FIG. 4, a spatial accuracy correction apparatus 90 uses aCMM 10, a tracking-type laser interferometer 20, and a PC 99. Thespatial accuracy of the CMM 10 is to be corrected.

The CMM 10 includes a Z spindle 102 to which a measurement probe 101 isaffixed, an X guide 103 holding the Z spindle 102 so as to be capable ofdisplacement in an X direction, and a column 104 to which the X guide103 is affixed and which is capable of displacement in a Y direction.Also, although not shown in the drawings, the CMM 10 further includes,for example, a Y displacement mechanism displacing the column 104 in theY direction, an X displacement mechanism displacing the Z spindle 102over the X guide 103 in the X direction, a Z displacement mechanismdisplacing the Z spindle 102 in a Z direction, and various scales whichmeasure the spatial coordinates of the measurement probe 101 and the Zspindle 102 based on an amount of displacement of each displacementmechanism, for example. A retroreflector 105 is also installed at a tipof the measurement probe 101. The measurement probe 101 may also bedetached and the retroreflector 105 mounted to a tip position of the Zspindle 102.

The tracking-type laser interferometer 20 is installed within ameasurement range of the CMM 10, or in the vicinity thereof. Thetracking-type laser interferometer 20 tracks the retroreflector 105 andmeasures a distance from a rotation center M of the tracking-type laserinterferometer 20 to the retroreflector 105.

The PC 99 is a computer connected to the CMM 10 and the tracking-typelaser interferometer 20. The PC 99 controls the CMM 10 and thetracking-type laser interferometer 20, and simultaneously performscoordinate measurement with the CMM 10 and length measurement with thetracking-type laser interferometer 20.

In this example, the tracking-type laser interferometer 20 normallycannot measure an absolute distance. Accordingly, using the methoddescribed in German Patent No. 102007004934, a position M of a rotationcenter of a tracking-type laser interferometer (hereafter abbreviated asa rotation center M) and an absolute distance from the rotation center Mto the retroreflector 105 are calculated with the multilaterationmethod. Then, a measured length value d acquired by the tracking-typelaser interferometer 20 is preset such that the measured length value dindicates the absolute distance from the rotation center M to theretroreflector 105. However, coordinates (x_(m), y_(m), z_(m)) of therotation center M that are calculated at this point and a preset valueof the measured length value d acquired by the tracking-type laserinterferometer 20 are values found with the accuracy of the CMM 10 priorto correction and are not very accurate values. Therefore, when aspatial accuracy correction parameter Bα (hereafter abbreviated as acorrection parameter Bα) for the CMM 10 is calculated, correctionconstants can be respectively applied to each value as an unknownquantity, and the optimal solution for the correction constants can becalculated together with the correction parameter Bα.

After the presetting described above, the position of the retroreflector105 (hereafter referred to as a measurement point X) is modified and aplurality of the measurement points X are measured. Then, after that, astylus offset (relative position of the retroreflector 105 with respectto the tip of the Z spindle 102 of the CMM 10) and the position of therotation center M of the tracking-type laser interferometer(installation position of the tracking-type laser interferometer 20) aremodified, and a plurality of measurement points X (a total of severalthousand points) are measured. After the position of the rotation centerM is modified, and after the stylus offset is modified, the coordinatesof the rotation center M and the preset value of the measured lengthvalue d change, and therefore presetting is performed again. Therefore,a different value is applied to the position of the rotation center M(x_(m), y_(m), z_(m)) and the preset value of the measured length valued each time the position of the rotation center M changes, and each timethe stylus offset changes.

In the measurement of the measurement point X, a measured value X_(CMM)(x_(CMM), y_(CMM), z_(CMM)) of the measurement point X acquired by theCMM 10 and the measured length value d acquired by the tracking-typelaser interferometer 20 are measured simultaneously. Also, because themultilateration method is used, the rotation center M of thetracking-type laser interferometer 20 changes to and is measured at atleast four different positions. Then, after the measurement of allmeasurement points X has ended, a correction parameter of the CMM 10 iscalculated from the measured data (X_(CMM), d). In the calculation ofthe correction parameter, the measured data measured at the severalthousand measurement points X is substituted into Expressions (1) and(2) below, simultaneous equations for the several thousand Expressions(1) and (2) are prepared, and the correction parameter Bα of the CMM 10is found by solving the equations using the least square method, as inUmetsu et al., for example.

$\begin{matrix}{\left\lbrack {{Formula}\mspace{14mu} 1} \right\rbrack \mspace{625mu}} & \; \\{{{\delta \; p} \equiv \begin{bmatrix}{\delta \; x} & {\delta \; y} & {\delta \; z}\end{bmatrix}^{T}} = {{HB}\; \alpha}} & (1) \\{\sqrt{\begin{matrix}{\left\{ {\left( {x_{CMM} + {\delta \; x}} \right) - \left( {x_{m} + f_{xm}} \right)} \right\}^{2} + \left\{ {\left( {y_{CMM} + {\delta \; y}} \right) - \left( {y_{m} + f_{ym}} \right)} \right\}^{2} +} \\\left\{ {\left( {z_{CMM} + {\delta \; z}} \right) - \left( {z_{m} + f_{zm}} \right)} \right\}^{2}\end{matrix}} = \left( {d + F_{d}} \right)} & (2)\end{matrix}$

In Expression (1), δp≡(ax, δy, δz)^(T) is a matrix of an error in themeasured values X_(CMM) acquired by the CMM 10 at each measurement pointX, and specifically is an error between the actual position of theretroreflector 105 and the measured value X_(CMM). The superscriptcharacter “T” represents a transposed matrix. Bα is a matrix ofcorrection parameters for the CMM 10 expressed by a B-spline function, Bis a matrix of basis functions of B-spline functions, and a is a matrixof coefficients for the basis functions. H is a matrix converting thecorrection parameter Bα to an error δp of the measured value X_(CMM),and is a known matrix configured from a mechanical structure and stylusoffset information for the CMM 10 to be corrected. Also, the left andright sides of Expression (2) express, respectively, the measured valueX_(CMM) for the CMM 10 and the distance from the rotation center M tothe retroreflector 105, which is expressed by the measured length valued of the tracking-type laser interferometer 20. As noted in the abovedescription, x_(m), y_(m), and z_(m) are respectively x, y, and zcomponents of the coordinates of the rotation center M measured in thepresetting. F_(d) is a correction constant for the preset value of themeasured length value d (hereafter referred to as a first correctionconstant F_(d)), and f_(xm), f_(ym), and f_(zm) are respectively x, y,and z components of a correction constant F_(M) for the coordinates ofthe rotation center M (hereafter referred to as a second correctionconstant F_(M)). The first correction constant F_(d) and the secondcorrection constant F_(M) are both unknown quantities, and a differentcorrection constant is applied each time the position of the rotationcenter M of the tracking-type laser interferometer is changed and eachtime the stylus offset is changed. These correction constants can befound, together with the correction parameter Bα, when solving thesimultaneous equations of Expressions (1) and (2). The spatial accuracyof the CMM 10 to be corrected can be corrected using the correctionparameter Bα, which is found as described above.

Non-Patent Literature

-   Umetsu, Kenta and Ryosyu Furutnani, Sonko Osawa, Toshiyuki    Takatsuji, and Tomizo Kurosawa. “Geometric calibration of a    coordinate measuring machine using a laser tracking system.”    Measurement Science and Technology 16.12 (2005): 2466-2472.

In a spatial accuracy correction method such as that described above,the tracking-type laser interferometer 20 measures length with therotation center M as a reference point. However, when the position ofthe rotation center M becomes offset with respect to a coordinate originpoint of the CMM 10 due to temperature drift or an external impact, forexample, an error due to the positional offset of the rotation center Mmay be incorporated into the measured length value d of thetracking-type laser interferometer 20. In such a case, a determinationcannot be made as to whether the error described above is incorporatedinto the measured length value d and the effects of the positionaloffset of the rotation center M applied to the measured length value dcannot be inhibited by the methods of German Patent No. 102007004934 orUmetsu et al., described above. Accordingly, spatial accuracy correctionis performed with the error included, which presents an issue of beingunable to conduct a high-accuracy correction process.

SUMMARY OF THE INVENTION

The present invention provides a spatial accuracy correction method andapparatus having a high degree of correction accuracy.

A spatial accuracy correction method according to the present inventionis a method that includes a positioning mechanism displacing adisplacement body to a predetermined set of spatial coordinates, thepositioning mechanism also having a retroreflector mounted to thedisplacement body, and a laser interferometer having a reference pointand measuring a distance from the reference point to the retroreflector,the method performing spatial accuracy correction of the positioningmechanism using a measured length value measured by the laserinterferometer and a measured value for spatial coordinates of theretroreflector measured by the positioning mechanism. The methodincludes a measurement step in which the retroreflector is displaced tothe plurality of measurement points in order, and the measured lengthvalue and the measured value at each of the measurement points areacquired. In the measurement step, after measuring the measured lengthvalue and the measured value for each of the plurality of measurementpoints, at least one or more repeated measurement is conducted for atleast one of the plurality of measured measurement points. When an errorin the measured length value which is repeatedly measured with respectto the measurement point that has undergone the repeated measurement isequal to or greater than a predetermined threshold value, the pluralityof measurement points are measured again.

In this example, a repeat error can be found by a difference between themaximum value and the minimum value among the plurality of measuredlength values being acquired with respect to the measurement points thathave undergone the repeated measurement, for example. In the presentinvention, after measuring the measured value and the measured lengthvalue with respect to the plurality of measurement points, the repeatmeasurement is conducted for at least one of the measurement pointsbeing measured. Then, the repeat error of the measurement point that hasundergone the repeated measurement is determined whether the error isequal to or greater than a predetermined threshold value. When therepeat error is determined to be equal to or greater than the thresholdvalue, the measurement is conducted again for the plurality ofmeasurement points. When the repeat error is equal to or greater thanthe threshold value, position of the laser interferometer (position ofthe reference point) may be displaced due to temperature drift or anexternal impact and error is incorporated in the measured length value.In such a case, there is a possibility that the error is incorporatedinto the measurement points onward the measurement point that hasundergone the repeated measurement. When a correction parameter iscalculated based on the measured value before conducting the repeatedmeasurement, a high-accuracy correction cannot be performed. Incontrast, in the present invention, when the repeat error is equal to orgreater than the threshold value, measurement is conducted again for theplurality of measurement points. Accordingly, an appropriate measuredlength value can be acquired with respect to the each measured point andhigh accurate correction parameter can be calculated.

In the spatial accuracy correction method according to the presentinvention, preferably, in the measurement step, a plurality ofmeasurement points are divided into a plurality of measurement lines andafter measurement of the measured length value and the measured valuesof all the measured points belonging to each of the measurement lines isended, at least one or more repeated measurement is conducted for atleast one of the measurement points belonging to the measurement line.

In the present invention, the plurality of measurement points aredivided into a plurality of measurement lines that include apredetermined number Ka of measurement points for example, and therepeated measurement is conducted for each measurement line. In such acase, compared to a case where all the plurality of measurement pointsare measured again, appropriate measured value and measured length valuewith respect to the each measurement point can be acquired rapidly.

In the spatial accuracy correction method according to the presentinvention, preferably, the method includes a parameter calculation stepin which the correction parameter of the spatial accuracy correction ofthe positioning mechanism is calculated based on the measured value, themeasured length value, and the coordinates of the reference point of thelaser interferometer. In the parameter calculation step, the correctionparameter is preferably calculated by applying a first correctionconstant to the measured length value and a second correction constantto the coordinates of the reference point for each measurement line.

The first correction constant is a constant to correct deviation of themeasured length value and the second correction constant is a constantto correct the positional offset of the reference point coordinates ofthe laser interferometer. In the present invention, in the parametercalculation step, the second correction constant, which is respectivelydifferent for each measurement line is applied to the reference pointcoordinate of the laser interferometer of each measurement point and thefirst correction constant, which is respectively different for each lineis applied to measured length value. In such a case, for example,measured value and the measured length value with respect to eachmeasurement point is substituted into Expressions (1) and (2) mentionedabove and simultaneous equation is prepared and appropriate value forthe first correction constant and the second correction constant andcorrection parameter Bα can be found simultaneously by solving thesimultaneous equation. In such a case, for example, in a case where thepositional offset of the reference point of the laser interferometer (arotation center M of a tracking-type laser interferometer described inGerman Patent No. 102007004934, for example) gradually increases duringmeasurement, the first correction constant and the second correctionconstant, which are respectively different for each measurement line,are applied and therefore, the influence can be inhibited, and a highlyaccurate correction parameter can be calculated.

In the spatial accuracy correction method of the present invention, atleast one or more measurement points that undergo the repeatedmeasurement is preferred to include the measurement point initiallymeasured on the measurement line. In the present invention, when therepeated measurement is conducted, the initial measurement point beingmeasured is included as a measurement point for the repeatedmeasurement. When the position of the tracking-type laser interferometerbecomes offset due to temperature drift or an external impact duringmeasurement of the plurality of measurement points, the measured lengthvalue from the repeated measurement at the measurement point initiallybeing measured is always different from the measured length value priorto the repeated measurement. Therefore, by having the measurement pointinitially being measured undergo the repeated measurement, adetermination can be made easily and rapidly whether the measurementshould be conducted again for the plurality of measurement points.

According to the spatial accuracy correction method of the presentinvention, in the repeated measurement, preferably, the plurality ofmeasurement points are measured in a reverse order of the measurement ofthe plurality of measurement points being measured most recently. In thepresent invention, when the repeated measurement is conducted,measurement is conducted in the reverse order of the measurement of theplurality of measurement points being recently measured. Accordingly,when the measured length value is gradually increased or decreased bytemperature drift and the like, for example, it is possible to cancelout the effect by temperature drift by finding the least square valuebetween the measured length value at each measurement point from therepeated measured and the measured length value of each of recentmeasurement points, for example. In addition, when temperature drift isoccurred while the repeated measurement is conducted, compared to a casewhere the measured length value is acquired by displacing each of themeasurement points in the same direction with the recent measurementpoint, a case where the measured length value is acquired by displacingthe measurement points in the reverse order causes a greater repeaterror. For example, measurement is conducted in order from a measurementpoint X₁ to a measurement point X_(Ka), and the measurement is conductedin order from the measurement point X_(Ka) to the measurement point X₁in the repeated measurement, the difference (repeat error) between themeasured length value during the repeated measurement and the recentmeasured length value at X₁ is increased when temperature drift occurs.Therefore, the determination whether to conduct a measurement again foreach measurement point, that is, the determination whether the error isincluded in the measured length value due to displacement of therotation center M can be appropriately made, and a highly accuratespatial accuracy correction can be performed.

In the spatial accuracy correction method according to the presentinvention, before conducting the measurement step, preferably, apreliminary measurement step is included, in which a plurality of therepeated measurements are conducted for the plurality of measurementpoints and the threshold value is calculated based on the standarddeviation of the error by the repeated measurement of the plurality ofmeasurement points in the preliminary measurement step. In the presentinvention, the preliminary measurement step is conducted prior to themain measurement and the measured length value for each measurementpoint is measured repeatedly. Then, the threshold value is defined basedon the standard deviation of the repeat error by the repeatedmeasurement (for example, a value which is three times the standarddeviation is set as a threshold value). In such a case, compared to acase where a predetermined threshold value is used, it is possible toset the most appropriate threshold value in accordance with measurementenvironment.

The spatial accuracy correction method according to the presentinvention is a method that includes a positioning mechanism displacing adisplacement body to a predetermined set of spatial coordinates, thepositioning mechanism also having a retroreflector mounted to thedisplacement body and allows measurement of measured value of spatialcoordinates of the retroreflector; a laser interferometer having thereference point and measuring a measured length value that is a distancefrom the reference point to the retroreflector; and a control devicethat is connected to the positioning mechanism and the laserinterferometer. The control device displaces the retroreflector to theplurality of measurement points in order and acquires the measuredlength value and measured value being measured at each of themeasurement points. After measuring the measured length value andmeasured value with respect to each of the plurality of measurementpoints, at least one or more repeated measurement is conducted for atleast one of the plurality of measurement points being measured and whenthe error in the measurement length value from the repeated measurementwith respect to the measurement points being measured repeatedly isequal to or greater than the predetermined threshold value, theplurality of measurement points are measured again. In the presentinvention, similar to those of the above-described inventions, when therepeat error is equal to or greater than the threshold value,measurement is conducted again for the plurality of measurement points.Accordingly, an appropriate measured length value can be acquired withrespect to the each measured point and high accurate correctionparameter can be calculated.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is further described in the detailed descriptionwhich follows, in reference to the noted plurality of drawings by way ofnon-limiting examples of exemplary embodiments of the present invention,in which like reference numerals represent similar parts throughout theseveral views of the drawings, and wherein:

FIG. 1 illustrates a schematic configuration of a spatial accuracycorrection apparatus according to a first embodiment;

FIG. 2 is a flow chart illustrating a spatial accuracy correction methodaccording to the first embodiment;

FIG. 3 is a flow chart illustrating a measuring process of the firstembodiment;

FIG. 4 illustrates an exemplary measurement order of measurement pointsaccording to the first embodiment;

FIG. 5 illustrates an exemplary measurement order of measurement pointsaccording to a third embodiment;

FIG. 6 illustrates a schematic view of a configuration of functions of acontrol device according to a fourth embodiment; and

FIG. 7 illustrates a schematic configuration of a conventional spatialaccuracy correction apparatus.

DETAILED DESCRIPTION OF THE INVENTION

The particulars shown herein are by way of example and for purposes ofillustrative discussion of the embodiments of the present invention onlyand are presented in the cause of providing what is believed to be themost useful and readily understood description of the principles andconceptual aspects of the present invention. In this regard, no attemptis made to show structural details of the present invention in moredetail than is necessary for the fundamental understanding of thepresent invention, the description taken with the drawings makingapparent to those skilled in the art how the forms of the presentinvention may be embodied in practice.

First Embodiment

Hereafter, a spatial accuracy correction apparatus according to anembodiment of the present invention is described. FIG. 1 illustrates aschematic configuration of a spatial accuracy correction apparatus 1according to the embodiment. The spatial accuracy correction apparatus 1includes a CMM 10, a tracking-type laser interferometer 20, and acontrol device 30. In FIG. 1, the CMM 10 and the tracking-type laserinterferometer 20 have the same configuration as the conventionalexample illustrated in FIG. 4. Specifically, the CMM 10 is equivalent toa positioning mechanism or machine in the present disclosure, andincludes a measurement probe 101, a Z spindle 102 to which themeasurement probe 101 is affixed, an X guide 103 holding the Z spindle102 so as to be capable of displacement in an X direction, and a column104 to which the X guide 103 is affixed and which is capable ofdisplacement in a Y direction. In addition, the CMM 10 includes a Ydisplacement mechanism, an X displacement mechanism, a Z displacementmechanism, and various scales, none of which are shown in the drawings.The CMM 10 also positions the measurement probe 101 (displacement bodyor displacer) by displacing the measurement probe 101 to a positionhaving predetermined spatial coordinates, and measures the spatialcoordinates of the positioned measurement probe 101 as a measured valueX_(CMM). In the present embodiment, by controlling the Y displacementmechanism, X displacement mechanism, and Z displacement mechanism, themeasurement probe 101 and the Z spindle 102 to which the measurementprobe 101 is affixed are displaced in XYZ directions, configuring thedisplacement body of the present invention. Moreover, a retroreflector105 that reflects laser light from the tracking-type laserinterferometer 20 is mounted at a tip position of the measurement probe101 configuring the displacement body. The measurement probe 101 mayalso be detached and the retroreflector 105 mounted to a tip position ofthe Z spindle 102.

The tracking-type laser interferometer 20 is equivalent to a laserinterferometer in the present invention, and is installed within ameasurement range of the CMM 10 (a table 106 or the like on which ameasured object is placed, for example) or in the vicinity thereof.Although not shown in the drawings, the tracking-type laserinterferometer 20 includes, for example, a laser light source that emitslaser light, a light separator that separates the laser light intomeasurement light and reference light, a light receiver receivinginterfering light that is a composite of the reference light and laserlight reflected by the retroreflector 105 (return light), and a two-axisrotation mechanism that controls an emission direction of themeasurement light (laser light). In addition, the tracking-type laserinterferometer 20 tracks the retroreflector 105 by controlling thetwo-axis rotation mechanism, such that an optical axis of the returnlight reflected by the retroreflector 105 coincides with an optical axisof the emitted light. More specifically, the two-axis rotation mechanismincludes a horizontal rotation mechanism that rotates the emissiondirection of the laser centered around a perpendicular axis that isparallel to a Z axis and sweeps the emission direction of the laser in ahorizontal direction, and a Z rotation mechanism that causes rotationcentered around a horizontal axis that is orthogonal to theperpendicular axis and sweeps the emission direction of the laser in theZ direction. Also, a point of intersection between the perpendicularaxis and the horizontal axis is a rotation center M of the tracking-typelaser interferometer 20, and serves as a reference point in the presentinvention. The tracking-type laser interferometer 20 uses theinterference between the reference light and the return light from theretroreflector 105 to measure a distance from the rotation center M ofthe two-axis rotation mechanism to the retroreflector 105. The distancemeasured by the tracking-type laser interferometer 20 is designated as ameasured length value d.

The control device 30 is connected to both the CMM 10 and thetracking-type laser interferometer 20. Also, the control device 30controls the CMM 10 and the tracking-type laser interferometer 20,acquires the measured value X_(CMM) for the position of theretroreflector 105 from the CMM 10 and the measured length value d fromthe tracking-type laser interferometer 20, respectively, and performs aspatial accuracy correction process of the CMM 10.

Specifically, the control device 30 is configured by a computer such asa personal computer, and includes, for example, storage configured by amemory or the like and a calculator configured by a CPU (CentralProcessing Unit) or the like. Also, as shown in FIG. 1, the calculatorretrieves and executes a program stored in the storage, and thecontroller 30 thereby carries out operations as a measurement pointcontroller 31, a measurement result acquirer 32, an error determiner 33,a correction value calculator 34, and the like.

The measurement point controller 31 displaces the retroreflector 105 toa predetermined measurement point X. In the present embodiment, aplurality of measurement points at which measurement is conducted and ameasurement order for the measurement points are defined ahead of time.In this example, in the present embodiment, the plurality of measurementpoints are divided into a plurality of measurement lines that include apredetermined number Ka of measurement points, and the measurement pointcontroller 31 measures each of the measurement points belonging to themeasurement line in order, then measures again (repeated measurement) atleast one of the measurement points belonging to the measurement line.

The measurement result acquirer 32 acquires the measurement results foreach measurement point. In other words, the measurement result acquirer32, for example, synchronizes the CMM 10 and the tracking-type laserinterferometer 20, and causes the measured value X_(CMM) and themeasured length value d for the measurement point X to be measuredsimultaneously. The measurement probe 101 may also be stopped at themeasurement point X by the measurement point controller 31 and themeasured value X_(CMM) and the measured length value d may be measuredat substantially the same time.

The error determiner 33 calculates, with respect to the measurementpoint repeatedly measured, a difference (repeat error Δd_(C1)) betweenthe measured length value d measured repeatedly and the measured lengthvalue d initially measured (before the repeated measurement) anddetermines whether the repeat error Δd_(C1) exceeds a threshold value S.The correction value calculator 34 calculates a correction parameter Bαbased on the measured value X_(CMM) and the measured length value dacquired by the measurement result acquirer 32. Detailed processes ofthe measurement point controller 31, the measurement result acquirer 32,the error determiner 33, and the correction value calculator 34 aredescribed later.

Spatial Accuracy Correction Method

Hereafter, a spatial accuracy correction method (spatial accuracycorrection process) performed by the spatial accuracy correctionapparatus 1 is described in which a correction parameter for correctingthe spatial coordinates of the CMM 10 is calculated. In the spatialaccuracy correction process according to the present embodiment, theposition of the rotation center M of the tracking-type laserinterferometer 20 (installation position of the tracking-type laserinterferometer 20) and a stylus offset (relative position of theretroreflector 105 with respect to the Z spindle) are modified and themeasured values X_(CMM) and measured length values d for the pluralityof measurement points X are acquired, and the correction parameter Bα iscalculated. In this example, the present embodiment is described ashaving a variable that indicates the stylus offset designated n (where nis an integer from 1 to n_(max) and an initial value is n=1) and avariable that indicates the position of the rotation center M of thetracking-type laser interferometer 20 designated m (where m is aninteger from 1 to m_(max) and an initial value is m=1).

FIG. 2 is a flow chart illustrating the spatial accuracy correctionprocess (spatial accuracy correction method) according to the presentembodiment. In the spatial accuracy correction process according to thepresent embodiment, first, the position of the rotation center M of thetracking-type laser interferometer 20 is set to an m^(th) installationposition (step S1). The stylus offset (position of retroreflector 105)is set to a position of an n^(th) offset pattern (step S2). In steps S1and S2, an operator may, for example, manually modify the mount positionof the retroreflector 105 and the installation position of thetracking-type laser interferometer 20, or the mount position of theretroreflector 105 and the installation position of the tracking-typelaser interferometer 20 may be modified automatically. For example, amotorized probe that is capable of modifying an orientation of thestylus using electric drive may be used as the measurement probe 101,and the relative position of the retroreflector 105 with respect to theZ spindle 102 may be displaced through control executed by the controldevice 30. In addition, the tracking-type laser interferometer 20 may beheld by a movable arm that is capable of displacing with respect to theXYZ directions, and the installation position of the tracking-type laserinterferometer 20 may be set to a predetermined position by controllingthe movable arm through control executed by the control device 30. Afterthis, the control device 30 conducts a measurement process (measurementstep) of the measured values X_(CMM) and the measured length values dfor the plurality of measurement points X (step S3).

FIG. 3 is a flow chart illustrating a measuring process for the measuredvalues X_(CMM) and the measured length values d of the plurality ofmeasurement points X according to the present embodiment. In themeasuring process of step S3, similar to a conventional spatial accuracycorrection process, first presetting is performed in which the positionof the rotation center M of the tracking-type laser interferometer 20and an absolute distance from the rotation center M to theretroreflector 105 are defined (step S11). In step S11, as in thespecification of German Patent No. 102007004934 and Umetsu et al.(2005), for example, a multilateration method is used to calculate thecoordinates of the rotation center M and the absolute distance from therotation center M to the retroreflector 105, and presetting is performedsuch that the measured length value d acquired by the tracking-typelaser interferometer 20 equals the absolute distance from the rotationcenter M to the retroreflector 105.

Next, the control device 30 controls the CMM 10, displaces theretroreflector 105 to the plurality of measurement points X, andconducts a measurement with the CMM 10 and a length measurement with thetracking-type laser interferometer 20 for each of the measurement pointsX. For these measurements, the control device 30 first sets a variable athat indicates the measurement line to an initial value (a=1) (stepS12), then sets a variable A that indicates the measurement point Xbelonging to each measurement line to an initial value (A=1) (step S13).The variable a is an integer from 1 to a_(max), and “measurement lineL_(a)” indicates an a^(th) measurement line L. Furthermore, the variableA is an integer from 1 to Ka, and a measurement point X_(A) indicates ameasurement point X that is measured A^(th) on the measurement line. Thenumber Ka of measurement points X included in the measurement line L maybe a different value for each measurement line L, or may be the samevalue for each.

Also, the measurement point controller 31 controls the CMM 10 anddisplaces the retroreflector 105 to a measurement point X_(A) on ameasurement line L_(a) (step S14). The measurement result acquirer 32measures the measurement point X_(A) on the measurement line L_(a) withthe CMM 10 and the tracking-type laser interferometer 20, and acquiresthe measured value X_(CMM) measured by the CMM 10 and the measuredlength value d measured by the tracking-type laser interferometer 20,respectively (step S15). In step S15, the CMM 10 and the tracking-typelaser interferometer 20 may be synchronized and the measured valueX_(CMM) and the measured length value d may be acquired simultaneously;the retroreflector 105 may also be stopped at a position correspondingto the measurement point X_(A) and the measurement by the CMM 10 and themeasurement by the tracking-type laser interferometer 20 may be carriedout in order.

After this, the measurement point controller 31 determines whether thevariable A equals Ka (step S16). Specifically, the measurement pointcontroller 31 determines whether measurement for all (for Ka) of themeasurement points X belonging to the measurement line L_(a) has ended.When the measurement point controller 31 reaches a “No” determination instep S16, 1 is added to the variable A (step S17) and the processreturns to step S14. That is, measurement points X at Ka points from A=1to A=Ka belonging to the measurement line L_(a) are measured insuccession. For example, in the example of FIG. 4, a number K1 ofmeasurement points X belong to the measurement line L₁ and the measuredvalue X_(CMM) and measured length value d are measured in order from ameasurement point X₁, measurement point X₂, measurement point X₃, . . .measurement point X_(K1-1), and a measurement point X_(K1).

On the other hand, when the measurement point controller 31 reaches a“Yes” determination in step S16, the measurement point controller 31displaces the retroreflector 105 to a predetermined measurement pointX_(Ca) on the measurement line L_(a) (step S18). Then, the measurementresult acquirer 32 conducts the repeated measurement at the measurementpoint X_(Ca) by the tracking-type laser interferometer 20 (step S19). Inthe present embodiment, the measurement point X_(Ca) to be measured forrepeated measurement is the measurement point X₁. In other words, on themeasurement line L_(a), the measurement point controller 31 displacesthe retroreflector 105 to a position of the measurement point X₁ thathas been initially measured and conducts measurement on the measurementpoint X₁ by the tracking-type laser interferometer 20. Accordingly, asshown in FIG. 4, when measurement of the measurement point X_(K1) on themeasurement line L₁ is ended, not the measurement of the measurementpoint X₁ on a measurement line L₂, but the measurement of the measuredlength value d with respect to the measurement point X₁ on themeasurement line L₁ is repeated. The number of measurements of therepeated measurement in step S19 may be once or may be two times ormore. Even when the measurement is conducted once in step S19, themeasurement with respect to the measurement point X_(Ca) is conductedtwo times in total by measurements in steps S15 and S19.

Next, the error determiner 33 determines, based on the measurementresults of the repeated measurement in step S19, whether a repeat errorΔd is equal to or greater than a predetermined threshold value S (stepS20). Specifically, the error determiner 33 extracts the largestmeasured value d_(max) _(_) _(Ca) and the smallest measured valued_(min) _(_) _(Ca) from the measured length value d acquired bymeasurement in step S15 and at least one or more measured length valuesd acquired by the repeated measurement in step S19. Then, the errordeterminer 33 determines whether a repeat error Δd_(Ca) (=d_(max) _(_)_(Ca)−d_(min) _(_) _(Ca)) is equal to or greater than the predeterminedthreshold value S.

When the error determiner 33 reaches a “Yes” determination (Δd_(Ca)≥S)in step S20, and the process returns to step S13. In other words, themeasurement point controller 31 controls the CMM 10 and displaces theretroreflector 105 to the initial measurement point X₁ on themeasurement line La, and measures again the measured value X_(CMM) andmeasured length value d from measurement points X₁ to X_(Ka). Thus,measurement of each measurement point X belonging to the measurementline L_(a) is repeated until it is determined as Δd_(Ca)<S in step S20.

Meanwhile, when the measurement point controller 31 reaches a “No”determination (Δd_(Ca)<S) in step S20, the measurement point controller31 determines whether the variable a equals a_(max) (step S21). When themeasurement point controller 31 reaches a “No” determination in stepS21, 1 is added to the variable a (step S22) and the process returns tostep S13. Specifically, each measurement point X belonging to the nextmeasurement line L_(a) are measured until the repeat error Δd_(Ca) isless than the threshold value S.

In an example shown in FIG. 4, measurements are conducted with respectto the measurement line L₁ for the measured values X_(CMM) and measuredlength values d from the measurement points X₁ to X_(K1) in order from(i) to (iv) by the measurements in step S13 to step S17. Then, as shownby (v) in FIG. 4, the repeated measurement is conducted by returning tothe measurement point X₁. In the example shown in FIG. 4, the calculatedrepeat error Δd_(C1) with respect to the measurement line L₁ is lessthan the threshold value S. In such a case, as shown in FIG. 4, afterconducting the repeated measurement of the measurement point X₁, withoutconducting measurement of the measurement points X₁ to X_(K1) again, ameasured object is moved to the initial measurement point X₁ on themeasurement line L₂ as shown by (vi) and the measurement for eachmeasurement point X belonging to the measurement line L₂ begins.

Also, similar to the measurement line L₁, measurements are alsoconducted with respect to the measurement line L₂ for the measuredvalues X_(CMM) and measured length values d from the measurement pointsX₁ to X_(K2) in order from (i) to (iv) by the measurements in step S13to step S17, after which the repeated measurement is conducted afterreturning to the measurement point X₁ shown by (v). In the example shownin FIG. 4, a calculated repeat error Δd_(C2) with respect to themeasurement line L₁ is equal to or greater than the threshold value S.In such a case, as shown by (vi) to (ix) in FIG. 4, after measurement ofthe measurement point X₁ is repeated, the measurements in step S13 toS17 are conducted again and the measured value X_(CMM) and measuredlength value d for each measurement point X from the measurement pointsX₁ to X_(K2) are measured again. Further, as shown by (x), the repeatmeasurement of the measurement X₁ and determination of the repeat errorΔd_(C2) are performed again. When the repeat error Δd_(C2) is determinedto be less than the threshold value S, the process advances to the nextmeasurement line L₃ as shown by (xi).

Then, when the measurement point controller 31 reaches a “Yes”determination in step S21, and the measured values X_(CMM) and measuredlength values d for all of the measurement points X in all of themeasurement lines L have been measured, the measurement process is endedfor a case where the stylus offset is an nth offset pattern and the setposition of the tracking-type laser interferometer 20 is an m^(th)position.

After this, the control device 30 determines whether the variable nequals n_(max) (step S4), and when the control device 30 reaches a “No”determination, 1 is added to the variable n (step S5) and the processreturns to step S2. In addition, when a “Yes” determination is made instep S4, the control device determines whether the variable m equalsm_(max) (step S6). When a “No” determination is made, 1 is added to thevariable m and the variable n is set to the initial value of 1 (step S7)and the process returns to step S1. Then, in step S6, when a “Yes”determination is reached, the correction value calculator 34 uses themeasured value X_(CMM) and the measured length value d and calculates acorrection parameter (step S8: parameter calculation step). In step S8,similar to a conventional spatial accuracy correction method, thecontrol device 30 applies the several thousand measured values X_(CMM)(x_(CMM), y_(CMM), z_(CMM)) and measured length values d measured by themeasuring process of step S3 into Expressions (1) and (2), which isgiven below, and simultaneous equations for several thousand Expressions(1) and (2) are generated.

$\begin{matrix}{\left\lbrack {{Formula}\mspace{14mu} 2} \right\rbrack \mspace{625mu}} & \; \\{{{\delta \; p} \equiv \begin{bmatrix}{\delta \; x} & {\delta \; y} & {\delta \; z}\end{bmatrix}^{T}} = {{HB}\; \alpha}} & (1) \\{\sqrt{\begin{matrix}{\left\{ {\left( {x_{CMM} + {\delta \; x}} \right) - \left( {x_{m} + f_{xm}} \right)} \right\}^{2} + \left\{ {\left( {y_{CMM} + {\delta \; y}} \right) - \left( {y_{m} + f_{ym}} \right)} \right\}^{2} +} \\\left\{ {\left( {z_{CMM} + {\delta \; z}} \right) - \left( {z_{m} + f_{zm}} \right)} \right\}^{2}\end{matrix}} = \left( {d + F_{d}} \right)} & (2)\end{matrix}$

In Expression (1), δp≡(δx, δy, δz)^(T) is a matrix of an error in themeasured values X_(CMM) acquired by the CMM 10 at each measurement pointX, and specifically is an error between the actual position of theretroreflector 105 and the measured value X_(CMM). The superscriptcharacter “T” represents a transposed matrix. In addition, Bα is amatrix of correction parameters for the CMM 10 expressed by a B-splinefunction, B is a matrix of basis functions of B-spline functions, and αis a matrix of coefficients for the basis functions. H is a matrixconverting the correction parameter Bα to an error δp of the CMM 10, andis configured from a mechanical structure and stylus offset informationof the CMM 10 to be corrected. In this example, the mechanical structureinformation for the CMM 10 is a value predetermined by individual CMM 10and the stylus offset information is a value predetermined by an offsetpattern with respect to the variable n set during measurement. Also, theleft and right sides of Expression (2) express, respectively, themeasured value X_(CMM) for the CMM 10 and the distance from the rotationcenter M to the retroreflector 105, which is expressed by the measuredlength value d of the tracking-type laser interferometer. And x_(m),y_(m), and z_(m) are respectively x, y, and z components of thecoordinates of the rotation center M measured in the presetting. Thefirst correction constant F_(d) is a correction constant for the presetvalue of the measured length value d. And f_(xm), f_(ym), and f_(zm) arerespectively x, y, and z components of the second correction constantF_(M). The second correction constant F_(M) is a correction constant forthe coordinate of the rotation center M. The first correction constantF_(d) and the second correction constant F_(M) are both unknownquantities, and a different correction constant is applied each time theposition of the rotation center M is changed and each time the stylusoffset is changed. These correction constants can be found, togetherwith the correction parameter Bα, when solving the simultaneousequations of Expressions (1) and (2). Therefore, the correction valuecalculator 34 allows the correction parameter Bα of the CMM 10 to befound by solving the simultaneous equations using the least squaremethod, for example.

Advantage of Present Embodiment

The spatial accuracy correction apparatus 1 according to the presentembodiment includes a CMM 10 which is a positioning mechanism; atracking-type laser interferometer 20 installed within a measurementrange of the CMM 10, or in the vicinity thereof; and a control device 30connected so as to be capable of communication with the CMM 10 and thetracking-type laser interferometer 20. In the spatial accuracycorrection process in which the spatial coordinates of the CMM 10 iscorrected, the control device 30 conducts the measurement step(measurement process) of the measured values X_(CMM) by the CMM 10 ateach measurement point X and the measured length values d by thetracking-type laser interferometer 20 by displacing the retroreflector105 to the plurality of measurement points X in order, theretroreflector 105 being provided at a tip position of the measurementprobe 101 of the CMM 10. At this time, the control device 30 divides theplurality of measurement points X into a plurality of measurement linesL_(a) (a=1˜a_(max)). After the measurement with respect to eachmeasurement point X belonging to the measurement line L_(a) is ended,the repeated measurement is conducted for the measured length value d ofthe predetermined measurement point X_(Ca) among the measurement pointsX belonging to the measurement line L_(a). Then, a determination is madewhether the repeat error Δd_(Ca) is equal to greater than the thresholdvalue S when the repeated measurement is conducted for the measurementX_(Ca). When the repeat error is equal to or greater than the thresholdvalue S, the measured value X_(CMM) and the measured length value d ofeach measurement point X belonging to the measurement line L_(a) aremeasured again. Accordingly, Δd_(Ca)≥S is realized when the position ofthe tracking-type laser interferometer 20 is displaced due totemperature drift or an external impact, and therefore, measurement ofeach measurement point X is conducted again. Accordingly, appropriatethe measured value X_(CMM) and the measured length value d of eachmeasurement point X can be acquired and the correction parameter Bα canbe calculated accurately in the spatial accuracy correction.

In addition, each time the measurement is ended for the number Ka ofmeasurement points X belonging to the measurement line L_(a) where theplurality of measurement points are divided, the repeated measurementfor the measurement point X_(Ca) belonging to the measurement line L_(a)is conducted. In such a case, for example, compared to a case where therepeated measurement for the predetermined measurement point X isconducted after the measurement of all measurement points X is conductedwithout setting the measurement line L_(a), appropriate measured valueand measured length value with respect to each measurement point X canbe acquired rapidly.

In the present embodiment, of the measurement points X belonging to themeasurement line L_(a), the measurement point X₁ being measured first onthe measurement line L_(a) is the measurement X_(Ca) where the repeatedmeasurement is conducted. In steps S14 and S15, the tracking-type laserinterferometer 20 may be displaced due to temperature drift or theexternal impact in the middle of measuring, in order, the measured valueX_(CMM) and measured length value d of each measurement point X of themeasurement line L_(a). In such a case, the repeated measurement of themeasurement point X₁ initially measured always includes the repeat errordue to positional offset. Therefore, by conducting repeated measurementof the measurement point X₁, the determination can be made rapidly andreadily whether the position of the tracking-type laser interferometer20 is displaced due to temperature drift or the external impact.

Second Embodiment

Next, a second embodiment is described. In the following description,portions identical to those which have been previously described areassigned identical reference numerals and a description thereof isomitted or simplified. According to the first embodiment describedabove, in the parameter calculation step in step S8, values of themeasured value X_(CMM) and measured length value d acquired in step S3are substituted into Expressions (1) and (2) and calculated thecorrection parameter by using the least square method. At this time,different correction constants were applied to the first correctionconstant F_(d) (correction constant of the measured length value d) andthe second correction constant F_(M) (correction constant of thecoordinates of the rotation center M) when the position of the rotationcenter M is changed and when the stylus offset is changed. In contrast,in a second embodiment, when the position of the rotation center M ischanged in addition to when the stylus offset is changed, as well aswhen the measurement line L_(a) is changed, different correctionconstants are applied to the first correction constant F_(d) and thesecond correction constant F_(M) respectively to calculate thecorrection parameter, which differs from the first embodiment.

In other words, the first embodiment enables detection of the offset inthe position of the rotation center M generated during a period from thetiming of initial measurement in step S15 until the repeated measurementis conducted in step S19. However, for example, in a case where theoffset in the position of the rotation center M increases (or decreases)over the measurement of the plurality of measurement lines L_(a),measurement accuracy is reduced. Given this, in the second embodiment, asecond correction constant F_(Ma) is applied to the position of therotation center M for each measurement line L_(a). In Addition, for eachmeasurement line L_(a), a first correction constant F_(da) is applied tothe measurement length value d of each measurement point X belonging tothe measurement line L_(a). The first correction constant F_(da) and thesecond correction constant F_(Ma) are set with respectively differentvalues (constant) for each measurement line L_(a).

After conducting the similar measurement as in the first embodiment, thecorrection value calculator 34 substitutes the several thousand measuredvalues X_(CMM) (x_(CMM), y_(CMM), z_(CMM)) and measured length values dinto Expression (1) and Expression (3), which is given below, andsimultaneous equations for several thousand Expressions (1) and (3) aregenerated. However, f_(xma), f_(yma), and f_(zma) are respectively x, y,and z components of the second correction constant F_(Ma).

$\begin{matrix}{\left\lbrack {{Formula}\mspace{14mu} 3} \right\rbrack \mspace{625mu}} & \; \\{\sqrt{\begin{matrix}{\left\{ {\left( {x_{CMM} + {\delta \; x}} \right) - \left( {x_{m} + f_{xma}} \right)} \right\}^{2} + \left\{ {\left( {y_{CMM} + {\delta \; y}} \right) - \left( {y_{m} + f_{yma}} \right)} \right\}^{2} +} \\\left\{ {\left( {z_{CMM} + {\delta \; z}} \right) - \left( {z_{m} + f_{zma}} \right)} \right\}^{2}\end{matrix}} = \left( {d + F_{da}} \right)} & (3)\end{matrix}$

Therefore, the correction value calculator 34 calculates the correctionparameter Bα by solving the simultaneous equations for Expressions (1)and (3) above using the least square method. At this time, an optimalsolution for the first correction constant F_(da) and the secondcorrection constant F_(Ma) are also calculated simultaneously.

In the present embodiment noted above, even when the position of thetracking-type laser interferometer 20 becomes offset due to atemperature drift or the like over measurement of the plurality ofmeasurement lines, by applying the correction constants F_(Ma) andF_(da) which are respectively different to each measurement line L_(a),the effects of the offset can be inhibited and highly accuratecorrection parameter can be calculated.

Third Embodiment

Next, a third embodiment is described. In the first embodiment describedabove, the measurement point X_(Ca) for the repeated measurement in stepS19 is the initial measurement point X₁ on the measurement line L_(a).In contrast, the third embodiment differs from the above-described firstembodiment in that the plurality of measurement points X belonging tothe measurement lines L_(a) are measured as the measurement pointX_(Ca).

FIG. 5 illustrates an exemplary measurement order of measurement pointsaccording to the third embodiment. Specifically, in the presentembodiment, the measurement point X_(Ca) for the repeated measurement isall the measurement points X included in the measurement lines L_(a) andthe measurement is conducted in a reverse direction from the recentmeasurement direction of the measurement points. In the example shown inFIG. 5, a number Ka of measurement points X belong to the measurementline L_(a), for example. In such a case, in step S15, in order from themeasurements points X₁, X₂, X₃ . . . to X_(Ka), that is, in order from(i), (ii), (iii) . . . to (iv) as illustrated by arrows shown in FIG. 5,the measurement is conducted for the number of Ka of measurement pointsX. On the other hand, in the repeated measurement in step S19, themeasurement is conducted in a reverse direction from the measurementorder in step S15 (measurement points from X_(Ka), X_(Ka-1), X_(Ka-3) .. . to X₁), that is, in order from (v), (vi) . . . to (vii), (viii) asillustrated by arrows in FIG. 5. When the repeated measurement isconducted a plurality of number of times, measurements are conductedalternately in the reverse direction and forward direction. The errordeterminer 33 calculates the repeat error Δd_(Ca) with respect to eachof the plurality of measurement points X_(Ca) (in the presentembodiment, all measurement points X belonging to the measurement lineL_(a)) and the measurement is conducted again when there is at least onerepeat error Δd_(Ca) being equal to or greater than the threshold valueS.

In this way, of the measurement points X belonging to the measurementline L_(a), by making the plurality of measurement points X for therepeated measurement, the offset in position of the tracking-type laserinterferometer 20 can be accurately determined. Further, during therepeated measurement, by measuring each measurement point in order ofthe reverse direction from the recent measurement order, an influence oftemperature drift can be inhibited effectively. In other words, in acase where temperature drift is generated during the repeatedmeasurement and the measurement of the plurality of measurement pointsX, an error may incorporated into the measured value acquired by therepeated measurement at each measurement point X as well. In contrast,when the measurements of each measurement point X are conductedalternately between in the forward direction and the reverse direction,for example, it is possible to substantially cancel the influence oftemperature drift and to acquire the measured length value close to whenthere is no temperature drift by calculating least square valuesthereof. While even in such a case, some offset error remains, however,by applying the correction constants F_(Ma) and F_(da) for eachmeasurement line L_(a) as in the second embodiment noted above, theoffset error can be reduced.

Fourth Embodiment

In the first embodiment noted above, the error determiner 33 uses thepredetermined threshold value S to determine whether the repeat errorΔd_(Ca) is Δd_(Ca)≥S. In contrast, the present embodiment differs fromthe first embodiment in that the threshold value S is changed inaccordance with results of the preliminary measurement.

FIG. 6 illustrates a schematic view of a configuration of functions ofthe control device according to a fourth embodiment. A control device30A of the present embodiment, similar to the first embodiment, servesas the measurement point controller 31, the measurement result acquirer32, the error determiner 33, the correction value calculator 34, andfurther serves as a threshold value definer 35. The threshold valuedefiner 35 defines the threshold value S based on the measurementresults when the preliminary measurement of the measured length value dfor each measurement point X is conducted.

Specifically, in the present embodiment, in the measurement process instep S3, after the presetting in step S11, the preliminary measurementis conducted before measuring (“the main measurement” of the measuredvalue X_(CMM) and the measured length value d with respect to eachmeasurement point X. In the preliminary measurement, the retroreflector105 is displaced in order of each measurement point X (X₁ to X_(Ka))belonging to the arbitrary measurement line L_(a) and measures themeasured length value d for each measurement point X, and further, therepeated measurement of each measurement point X of the measurement lineL_(a) is conducted again. After this, the threshold value definer 35calculates the repeat error Δd with respect to each measurement point Xand defines a value which is three times a standard deviation of therepeat error Δd as the threshold value S.

In the above, an example of defining the threshold value S is describedby the preliminary measurement of the arbitrary one measurement lineL_(a) (such as an initial measurement line L₁). However, the measurementmay be conducted for the plurality of measurement lines L_(a) and therepeated measurement of each measurement point X of all the measurementlines L_(a) (a=1˜a_(max)) may be conducted. In such a case, thethreshold value S of the measurement line L₁ may be defined based on theresult of the preliminary measurement of the measurement line L₁ and adifferent threshold value S may be defined for each measurement line.Further, in the preliminary measurement noted above, an example isdescribed where the initial measurement and one time repeatedmeasurement are conducted for each measurement point X (two measuredlength values d are acquired). However, by conducting more repeatedmeasurements, the threshold value S may be defined based on the repeaterror Δd_(Ca) calculated from at least three or more measured lengthvalues d.

In the present embodiment, the following effects and advantages can beachieved. In other words, when the predetermined value is used as thethreshold value S, for example, the threshold value S may be too smallor too large for operation environments or individual differences of theCMM 10 or the tracking-type laser interferometer 20. When the thresholdvalue S is too small, there is a case where the repeat error Δd_(Ca)does not become equal to or less than the threshold value S even afterrepeating the a plurality of processes from step S12 to step S20. Insuch a case, the longer time is required for the spatial accuracycorrection process. On the other hand, when the threshold value S is toolarge, the error included in the measured length value d is greater andthe highly accurate spatial accuracy correction process becomesdifficult. In response, in the present embodiment, the preliminarymeasurement of each measurement point X is conducted and based on theresult of the preliminary measurement, the threshold value determiner 35can define the most appropriate threshold value S in accordance with theoperation environments or the individual differences of the CMM 10 orthe tracking-type laser interferometer 20. Therefore, unfavorablesituation where the redetermined threshold value S is used as notedabove can be improved and the spatial accuracy correction process can beperformed rapidly and with a high degree of accuracy.

Modification

Moreover, the present invention is not limited to the embodimentdescribed above, but may include modifications within a scope notdeparting from the object of the present invention. For example, in thefirst to fourth embodiments, the CMM 10 is given as an example of apositioning mechanism, but the present invention is not limited to this.As noted above, any mechanism that positions a displacement body bydisplacing the displacement body to a predetermined set of spatialcoordinates can be employed as the positioning mechanism. For example,the positioning mechanism may be a machine tool having a processing toolthat cuts, polishes, or performs similar work on an object as thedisplacement body, where the machine tool displaces the processing toolto a predetermined coordinate position. The positioning mechanism mayalso be a transport robot having a gripping arm that grips an object asthe displacement body, where the transport robot transports the grippedobject to a predetermined position.

In the embodiments noted above, the plurality of measurement points Xare divided into a plurality of measurement lines L_(a), and each timethe measurement of the measurement line L_(a) is ended, an example isdescribed where the repeated measurement is conducted for at least onemeasurement points X belonging to the measurement line L_(a). However,the present invention is not limited to this. For example, each time themeasurement of a predetermined number (such as two) of measurement linesL_(a) is ended, the repeated measurement may be conducted for themeasurement points X included in the predetermined number of themeasurement lines L_(a). In addition, after measuring all themeasurement points X regardless of the measurement line L_(a), therepeated measurement of at least one measurement point (for example, themeasurement X₁ measured for the very first time) among the allmeasurement points X may be performed.

In the embodiment described above, an example is given in which thenumber of measurement points X (number Ka of measurement points)belonging to the measurement line L_(a) is a different value for eachmeasurement line L_(a), but the number of measurement points X belongingto each measurement line L_(a) may be an identical number Ka ofmeasurement points.

A method of defining the measurement points X belonging to themeasurement line L_(a) in the embodiment described above may be anymethod. For example, measurement points having a distance that is withina predetermined value from a preset reference measurement point may beincluded in a single measurement line L_(a). In other words, themeasurement points X that are positioned close to each other may beincluded in the same measurement line L_(a). Also, when the plurality ofmeasurement points are measured in order, the measurement lines L_(a)may be divided at the measurement points that can be measured within apredetermined amount of time. Specifically, the plurality of measurementpoints X that are measured within a predetermined first time t from thebeginning of the measurement are the measurement points X belonging tothe measurement line L₁, and the measurement points X that are measuredwithin a second time 2 t from the first time t are the measurementpoints X belonging to the measurement line L₂. Also, in such a case,time intervals for the measurement lines L_(a) are not necessarilyconstant. For example, the measurement points X that are measured withina first time t₁ from the beginning of the measurement may be designatedas the measurement points X belonging to the measurement line L₁, andthe measurement points X that are measured from the first time t₁ up toa second time t₂ (t₁≠t₂−t₁) may be designated as the measurement pointsX belonging to the measurement line L₂.

In the first embodiment, the initial measurement point X₁ belonging tothe measurement line L_(a) was for the repeated measurement, however,the object to be measured may be other measurement point X. However,when the repeated measurement is conducted, the repeat error becomes thelargest at the measurement point X measured in the first half on themeasurement line L_(a). Therefore, as the measurement point X for therepeated measurement, one of the measurement points X_(A) between A=1 toA=Ka/2 is preferably included. In addition, in the first embodiment, inaddition to the measurement point X₁, other measurement point X may beset as the measurement point X_(Ca) for the repeated measurement. Forexample, in steps S13 to S17, when the measured value X_(CMM) andmeasured length value d for the each measurement point X are measured inorder, the measurement points X that are measured at the odd numbers maybe the object for the repeated measurement.

In the second embodiment described above, an example is given where thefirst correction constant F_(da) is applied to the measured length valued of each measurement point X and the second correction constant F_(Ma)is applied to the coordinates of the rotation center M of thetracking-type laser interferometer 20. However, a correction constantmay also be applied to only one of the measured length value d and therotation center M. For example, when the first correction constantF_(da) is applied to only the measured length value d, in Expression (3)given above, simultaneous equations may be created with f_(xma),f_(yma), and f_(zma) set to 0 to find the correction parameter Bα.

In the fourth embodiment, the threshold value definer 35 calculates therepeat error Δd using the results of the repeated measurement conductedin the preliminary measurement, and defines a value which is three timesa standard deviation of the repeat error Δd as the threshold value S.However, the present invention is not limited to this. For example, avalue which is two times the standard deviation of the repeat error Δdmay be defined as the threshold value S, and further, the value may beacquired by adding a predetermined value to the standard deviation.

In each of the embodiments described above, the tracking-type laserinterferometer 20 having the rotation center M as the reference point isgiven as an example of a laser interferometer, but the present inventionmay also employ a laser interferometer that does not have a trackingfunction. However, each time a measurement point X is displaced, thelength measurement direction for measuring the distance with the laserinterferometer must be modified. Accordingly, in such a case,preferably, a plurality of measurement points are defined on the lengthmeasurement direction of the laser interferometer (on a straight line),and once the retroreflector 105 has been displaced to each measurementpoint, the measured value X_(CMM) and the measured length value d aremeasured. In addition, the length measurement direction is preferablychanged to a plurality of directions, and the plurality of measurementpoints X are preferably defined for each length measurement direction.

The present invention can be used for spatial accuracy correction of apositioning mechanism such as a coordinate measuring machine (CMM),machine tool, robot, or the like that positions a displacement body bydisplacing the displacement body to a predetermined coordinate position.

It is noted that the foregoing examples have been provided merely forthe purpose of explanation and are in no way to be construed as limitingof the present invention. While the present invention has been describedwith reference to exemplary embodiments, it is understood that the wordswhich have been used herein are words of description and illustration,rather than words of limitation. Changes may be made, within the purviewof the appended claims, as presently stated and as amended, withoutdeparting from the scope and spirit of the present invention in itsaspects. Although the present invention has been described herein withreference to particular structures, materials and embodiments, thepresent invention is not intended to be limited to the particularsdisclosed herein; rather, the present invention extends to allfunctionally equivalent structures, methods and uses, such as are withinthe scope of the appended claims.

The present invention is not limited to the above described embodiments,and various variations and modifications may be possible withoutdeparting from the scope of the present invention.

What is claimed is:
 1. A spatial accuracy correction method having apositioning mechanism displacing a displacement body to a predeterminedset of spatial coordinates, the positioning mechanism also having aretroreflector mounted to the displacement body, and a laserinterferometer having a reference point and measuring a distance fromthe reference point to the retroreflector, the method performing spatialaccuracy correction of the positioning mechanism using a measured lengthvalue measured by the laser interferometer and a measured value forspatial coordinates of the retroreflector measured by the positioningmechanism, the method comprising: a measurement process comprising:displacing the retroreflector to a plurality of measurement points inorder, and acquiring the measured length value and the measured value ateach of the measurement points, wherein after measuring the measuredlength value and the measured value for each of the plurality ofmeasurement points: conducting at least one or more repeated measurementfor at least one of the plurality of measured measurement points, andwhen an error in the repeated measurement of the measured length valuefor the measurement point that undergoes the repeated measurement isequal to or greater than a predetermined threshold value, againmeasuring the plurality of measurement points.
 2. The spatial accuracycorrection method according to claim 1, wherein the measurement processfurther comprises: dividing a plurality of measurement points into aplurality of measurement lines; and after measurement of the measuredlength value and the measured value of all the measured points belongingto each of the measurement lines is ended, conducting at least one ormore repeated measurements for at least one measurement point belongingto the measurement line.
 3. The spatial accuracy correction methodaccording to claim 2, further comprising: calculating a correctionparameter of the spatial accuracy correction of the positioningmechanism based on the measured value, the measured length value, andthe coordinates of the reference point of the laser interferometer,wherein the calculating of the correction parameter comprises applying afirst correction constant to the measured length value and a secondcorrection constant to the coordinates of the reference point for eachmeasurement line.
 4. The spatial accuracy correction method according toclaim 2, wherein at least one or more measurement point that undergoesthe repeated measurement includes the measurement point initiallymeasured on the measurement line.
 5. The spatial accuracy correctionmethod according to claim 3, wherein at least one or more measurementpoint that undergoes the repeated measurement includes the measurementpoint initially measured on the measurement line.
 6. The spatialaccuracy correction method according claim 2, wherein the conducting atleast one or more repeated measurements comprises measuring theplurality of measurement points in a reverse order of the measurement ofthe plurality of measurement points that are measured most recently. 7.The spatial accuracy correction method according claim 3, wherein theconducting at least one or more repeated measurements comprisesmeasuring the plurality of measurement points in a reverse order of themeasurement of the plurality of measurement points that are measuredmost recently.
 8. The spatial accuracy correction method according toclaim 1, further comprising: a preliminary measurement processcomprising conducting the repeated measurement a plurality of times forthe plurality of measurement points, before conducting the measurementprocess, wherein the threshold value is calculated based on a standarddeviation of error by the repeated measurement of the plurality ofmeasurement points in the preliminary measurement process.
 9. Thespatial accuracy correction method according to claim 2, furthercomprising: a preliminary measurement process comprising conducting therepeated measurement a plurality of times for the plurality ofmeasurement points, before conducting the measurement process, whereinthe threshold value is calculated based on a standard deviation of errorby the repeated measurement of the plurality of measurement points inthe preliminary measurement process.
 10. The spatial accuracy correctionmethod according to claim 3, further comprising: a preliminarymeasurement process comprising conducting the repeated measurement aplurality of times for the plurality of measurement points, beforeconducting the measurement process, wherein the threshold value iscalculated based on a standard deviation of error by the repeatedmeasurement of the plurality of measurement points in the preliminarymeasurement process.
 11. The spatial accuracy correction methodaccording to claim 4, further comprising: a preliminary measurementprocess comprising conducting the repeated measurement a plurality oftimes for the plurality of measurement points, before conducting themeasurement process, wherein the threshold value is calculated based ona standard deviation of error by the repeated measurement of theplurality of measurement points in the preliminary measurement process.12. The spatial accuracy correction method according to claim 5, furthercomprising: a preliminary measurement process comprising conducting therepeated measurement a plurality of times for the plurality ofmeasurement points, before conducting the measurement process, whereinthe threshold value is calculated based on a standard deviation of errorby the repeated measurement of the plurality of measurement points inthe preliminary measurement process.
 13. The spatial accuracy correctionmethod according to claim 6, further comprising: a preliminarymeasurement process comprising conducting the repeated measurement aplurality of times for the plurality of measurement points, beforeconducting the measurement process, wherein the threshold value iscalculated based on a standard deviation of error by the repeatedmeasurement of the plurality of measurement points in the preliminarymeasurement process.
 14. The spatial accuracy correction methodaccording to claim 7, further comprising: a preliminary measurementprocess comprising conducting the repeated measurement a plurality oftimes for the plurality of measurement points, before conducting themeasurement process, wherein the threshold value is calculated based ona standard deviation of error by the repeated measurement of theplurality of measurement points in the preliminary measurement process.15. A spatial accuracy correction apparatus comprising: a positioningmachine that displaces a displacer to a predetermined set of spatialcoordinates, the positioning machine comprising a retroreflector mountedto the displacer, the positioning mechanism being configured to measurea measurable value of the spatial coordinates of the retroreflector; alaser interferometer having a reference point and configured to measurea measurable length value that is a distance from the reference point tothe retroreflector; and a controller operably connected to thepositioning machine and the laser interferometer, the controllercomprising a processor and a memory that stores an instruction, whereinthe processor, when executing the instruction stored in the memory,performs operations comprising: displacing the retroreflector to aplurality of measurement points in order, acquiring the measured lengthvalue and measured value measured at each of the measurement points,conducting at least one or more repeated measurement for at least one ofthe plurality of measurement points being measured after conductingmeasurement of the measured length value and the measured value for eachof the plurality of measurement points, and when an error by therepeated measurement of the measured length value with respect to themeasurement point that has undergone the repeated measurement is equalto or greater than a predetermined threshold value, again measuring theplurality of measurement points.